Related papers: A Boundary Integral-based Neural Operator for Mesh…
Robot-assisted neurological surgery is receiving growing interest due to the improved dexterity, precision, and control of surgical tools, which results in better patient outcomes. However, such systems often limit surgeons' natural sensory…
We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…
Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing.…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. In many applications, the spatial distribution of a field needs to be…
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
A simple, yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced.…
The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid…
Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…
Latent Bayesian optimization (LBO) approaches have successfully adopted Bayesian optimization over a continuous latent space by employing an encoder-decoder architecture to address the challenge of optimization in a high dimensional or…
The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…
In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
Beamforming is an effective means to improve the quality of the received signals in multiuser multiple-input-single-output (MISO) systems. Traditionally, finding the optimal beamforming solution relies on iterative algorithms, which…
We consider the boundary value problems (BVPs) for linear secondorder ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the Cayley transform of the…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…
With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an…
Form-finding of unilateral membrane structures is commonly addressed by solving equilibrium equations with Finite Element Methods (FEMs). This paper investigates Physics-Informed Neural Networks (PINNs) as an alternative, where the…
This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…